Dynamic Analysis of a Modified Truck Chassis

Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4/ Summer - 21 31 Dynamic Analysis of a Modified Truck Chassis Mohammad Reza Forouzan Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran E-mail: Forouzan@cc.iut.ac.ir Rouhollah Hoseini* Department of Mechanical Engineering, Sharif University of Technology, Isfahan, Iran E-mail: R.Hoseini1987@gmail.com *Corresponding author Received 1 May 21; Revised 26 July 21; Accepted 18 September 21 Abstract: The paper investigates into the vibrational characteristics of the truck chassis including the natural frequencies and mode shapes. Truck chassis forms the structural backbone of a commercial vehicle. When the truck travels along the road, the truck chassis is excited by dynamic forces caused by the road roughness, engine, transmission and more. Modal analysis using Finite Element Method (FEM) can be used to determine natural frequencies and mode shapes. In this study, the modal analysis has been accomplished by the commercial finite element packaged ANSYS. The model has been simulated with appropriate accuracy and with considering the effect of bolted and riveted joints. The chassis has been altered by some companies for using in municipal service (street sweepers) and it raises the question: Are natural frequencies of the modified chassis in suitable range? After constructing finite element model of chassis and appropriate meshing with shell elements, model has been analyzed and first 6 frequencies that play important role in dynamic behavior of chassis, have been expanded. In addition, the relationship between natural frequencies and engine operating speed has been explained. The results show that the road excitation is the main disturbance to the truck chassis as the chassis natural frequencies lie within the road excitation frequency range. Finally advantages of the modified chassis which leads to the increase of the natural frequencies and placing them in the appropriate range, has been discussed. Keywords: Vibration, Truck chassis, Modal analysis, Dynamic, Finite elements Reference: M. R. Forouzan and R. Hoseini, (21), "Dynamic analysis of a modified truck chassis", Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4, pp. 33-38. Biographical notes: M.R. Forouzan received his PhD in Mechanical Engineering. He is currently Assistant Professor at the Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran. R. Hoseini is currently M.Sc student at Mechanical Engineering at the Sharif University of Technology, Tehran, Iran. 21 IAU, Majlesi Branch

32 Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4/ Summer - 21 1 INTRODUCTION The dynamic response of simple structures, such as uniform beams, plates and cylindrical shells, may be obtained by solving their equations of motion. However, in many practical situations either the geometrical or material properties vary, or the shape of the boundaries cannot be described in terms of known mathematical functions. Also, practical structures consist of an assemblage of components of different types, namely beams, plates, shells and solids. In these situations it is impossible to obtain analytical solutions to the equations of motion [1]. This difficulty is overcome by seeking some form of numerical solutions and finite element methods. Automotive industry is one of the biggest users of the technology of modal analysis. The modal behavior of car chassis is a part of most necessary information for the inspection into car's dynamic behavior. In this essay the modal analysis of truck chassis has been studied. As a truck travels along the road, the truck chassis is excited by dynamic forces induced by the road roughness, engine, transmission and more. Under such various dynamic excitations, the truck chassis tends to vibrate [2]. Whenever the natural frequency of vibration of a machine or structure coincides with the frequency of the external excitation, there occurs a phenomenon known as resonance, which leads to excessive deflections and failure. The literature is full of accounts of system failures brought about by resonance and excessive vibration of components and systems [3]. The global vibrational characteristic of a vehicle is related to both its stiffness and mass distribution. The frequencies of the global bending and torsional vibration modes are commonly used as benchmarks for vehicle structural performance. Bending and torsion stiffness influence the vibrational behavior of the structure, particularly its first natural frequency [4]. The mode shapes of the truck chassis at certain natural frequencies are very important to determine the mounting point of the components like engine, suspension, transmission and more. Therefore it is important to include the dynamic effect in designing the chassis [2]. Many researchers carried out study on truck chassis. Vasek and his cooperators (1998) have analysed a truck dynamically. In their method in addition to simulating truck with finite element packaged ANSYS and being sure that structure vibrational modes are in appropriate range, they vibrationally analyzed it [5]. Yuan Zhang and Arthur Tang (1998), compare natural frequencies of a ladder chassis with finite element and experimental methods [6]. Guo and chen (28), research into dynamic and modal analysis of a space chassis (complex 3-dimensional chassis) and analyse transient response using the principal of superposition [7].This paper deals with a 6 ton truck chassis that includes natural frequencies and mode shapes. This chassis has been shortened by related companies for using in municipal service (street sweeper) and here we face the challenge and it raises the question: Are natural frequencies of the modified chassis in suitable range? In the studied model unlike the most previous models, rivets and bolts have been modeled completely. Also shell element has been used for analysis. This element has better and more disciplined meshing in comparison with other elements and has the capability of gaining more accurate results with the same meshing containing the related 3-dimensional elements. It is mentionable that validity of the results has been verified by comparing the results from a similar model with the model proposed by Mr Foui and his cooperator [2]. 2 TRUCK CHASSIS In this article, a 6 ton truck chassis has been studied. This truck chassis is a ladder chassis and it's longitudinal and cross connecting sections are channel shaped. Automotive view with dimensional plan and dimensions has been illustrated in Fig.1 and Fig.2 and table 1. Chassis material is JIS-SAPH41 with 78 kg/m3 density and 52 MPa yield strength and 59 MPa tensile strength. Fig. 1 View of truck 21 IAU, Majlesi Branch

Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4/ Summer - 21 33 Fig. 2 Dimensional plane of truck EH 83 HH 21 OH1 222 CW 165 Table 1 Truck dimensions related to Fig.1 BW AW OW CA CE 2115 168 1995 3195 491 ROH 17 FOH 185 WB 3815 OAL1 66 3 FINITE ELEMENT MODEL Truck chassis has been modeled with 4-node shell element in ANSYS. Numerical studies on simple hollow rectangular beam show that this element is suitable for creating and meshing the model and it yields accurate results. The element used has 4 nodes with 6 degrees of freedom and is appropriate for linear and nonlinear deformations and also large deflections. There are approximately 7 elements in the model that has proved suitable in comparison with other cases, so that the error in each case is less than one percent. In Fig.3 and Fig.4 truck and chassis model have been shown. Model with appropriate accuracy and with considering bolts and riveted joints effects has been simulated. Meshes and constraints have been shown in Fig.6. Fig. 3 Geometric chassis model Fig. 5 Meshed chassis Fig. 4 Geometrical truck model The boundary conditions are different for each analysis. In normal mode analysis, free-free boundary condition will be applied to the truck chassis model, with no constraint applied to the chassis model [2]. A free-free boundary condition has been chosen as it is much simpler to test experimentally in this condition, if required. 21 IAU, Majlesi Branch

34 Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4/ Summer - 21 4 MODAL ANALYSIS AND RESULTS Modal analysis has been performed after creating the chassis finite element model and meshing in free-free state and with no constraints. The results have been calculated for the first 3 frequency modes and show that road simulations are the most important problematic for truck chassis. In this analysis we have made use of subspace method in ANSYS. Since chassis has no constraints, the first 6 frequency modes are vanished. 3 modes are related to the chassis displacement in x, y and z directions and 3 modes are related to chassis rotation about x, y and z axes. In Fig.6 related natural frequencies and mode shapes for chassis with maximum displacement in y direction in each mode, have been shown. 4th mode of frequency 5th mode of frequency 1st mode of frequency 6th mode of frequency Fig. 6 Natural frequencies of truck chassis 2nd mode of frequency 3rd mode of frequency The first, second and sixth modes are the global vibrations, while the others are local vibrations. local vibration starts at the third mode at 29.6 Hz. The dominant mode is a torsion which occurred at 7.219 Hz with maximum translation experienced by both ends of the chassis. The second mode is a vertical bending at 17.153 Hz. At this mode, the maximum translation is at the front part of the chassis. The third and fourth modes are localized bendings at 29.612 Hz and 33.517 Hz. The maximum translation is experienced by the top hat cross member. The member also experienced big translation at fifth mode which is a localized torsion mode. The top hat cross member is the mounting location of the truck gear box. The sixth mode is the 21 IAU, Majlesi Branch

Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4/ Summer - 21 35 torsion mode at 38.475 Hz with maximum translation at both ends of the chassis. Found natural frequencies from modal analysis of truck chassis, are used for determining the suitable situations for truck parts in working conditions. Figure 6 shows that twisting mode with the frequency of 7.219 Hz is the prevailing mode. Results of first 3 analyzed modes for chassis are shown in table 2. Table 2 natural frequencies per mode number Mode number Natural frequency 1 2 3 4 5 6 7 7.2195 8 17.153 9 29.612 1 33.517 11 35.161 12 38.475 13 42.347 14 46.692 15 48.857 16 67.16 17 77.469 18 82.553 19 88.42 2 93.7 21 96.135 22 1.43 23 14.93 24 16.79 25 115.14 26 117.26 27 127.19 28 127.93 29 133.8 3 154.39 Because the analysis is in free-free state, the first 6 modes that have zero frequency aren t considered and mode numbers 7 to 12 in table 2 represent the first 6 modes of frequency. It is necessary to notice that in usual, the first 6 modes of frequency (mode numbers 7 to 12 in table 2 that have been shown in Fig.6) play the main role in dynamic behavior of chassis and effects of higher frequencies, because of the increasing noises effects and limited energy of motor to generate these frequencies can be ignored. In general the natural frequency can be calculated using the equation (1); n K m (1) where K and m stand for stiffness and mass respectively. Diesel engine is known to have the operating speed varying from 8 to 33 revolutions per second (rps) [8]. In low speed idling condition, the speed range is about 8 to 1 rps. This translates into excitation frequencies varying from 24 to 3 Hz [2]. The main excitations are at low speeds, when the truck is in the first gear. At higher gear or speed, the excitations to the chassis are much less. The natural frequency of the truck chassis should not coincide with the frequency range of the axles, because this can cause resonance which may give rise to high deflection and stresses and poor ride comfort. Excitation from the road is the main disturbance to the truck chassis when the truck travels along the road. In practice, the road excitation has typical values varying from to 1 Hz. At high speed cruising, the excitation is about 3 rpm or 5 Hz. Mounting of vibration components of the truck on the nodal point of the chassis is one of the vibration attenuation methods to reduce the transmission of vibration to the truck chassis [2]. The mounting location of the engine and transmission system is along the symmetrical axis of the chassis s first torsion mode where the effect of the first mode is less. However, the mounting of the suspension system on the truck chassis is slightly away from the nodal point of the first vertical bending mode. This might due to the configuration of the static loading on the truck chassis. The equipment installed on the chassis of municipalservice truck increase the chassis mass which leads to the decrease of natural frequencies. Regarding the previous discussions about the diesel engine speed, we can say that natural frequencies are in critical range. Hence with decreasing the chassis length which increases the chassis stiffness, we increase the natural frequencies to place them in the appropriate range. In addition, with changing the gasoline tank situation and performing similar changes, we can prevent coinciding the simulation force frequencies and natural frequencies. Otherwise resonance phenomenon occurs and if these two frequencies coincide, this phenomenon destroys the chassis. As a reminder it is mentionable that validity of the results has been verified by comparing the results from a similar model with the model proposed by Mr Foui and his cooperator [2]. 21 IAU, Majlesi Branch

36 Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4/ Summer - 21 5 CONCLUSION REFERENCES The article has looked to changes of chassis dynamic behavior caused by change in usage with finite element method. First six frequency modes of the modified chassis that determine its dynamic behavior are below 4 Hz and vary from 7.22 to 38.475 Hz. For the first two modes and sixth mode, the truck chassis experienced global vibration. The global vibrations of the truck chassis include torsion and vertical bending with 2 nodal points. The local bending vibration occurs at the top hat cross member where the gearbox is mounted on it. Since chassis mass increases due to the installed equipment, the natural frequencies fall out of the natural range that can be compensated with increasing the chassis stiffness. Decreasing the chassis length, can increase the chassis stiffness. Using this method, we can prevent resonance phenomenon and unusual chassis vibration and place the natural frequencies in natural range. 6 ACKNOWLEDGMENTS [1] Fahi, F., and Walker, J., Advanced Applications in Acoustics, Noise and Vibration, 1st ed, spon press, London, 24. [2] Fui, T. H., Rahman, R. A., Statics and Dynamics Structural Analysis of a 4.5 Ton Truck Chassis, Jurnal Mekanikal, No. 24, 27, pp. 56-67. [3] Rao, S. S., Mechanical Vibration, 4 th Edition, pearson education press, 24. [4] Jason, C., Brown, A., John Robertson, Stan, T., Serpento, Motor vehicle structures, Butterworth-Heinemann, the University of Michigan, 22. [5] Vasek, M., Stejskal, V., Sika, Z., Vacalin, O., and, Kovanda, J., Dynamic Model of Truck for Suspension Control, Vehicle System Dynamic, Supplement 28, 1998, pp.496-55. [6] Zhang, Y., and Tang, A., New Approach for Vehicle System NVH Analysis, SAE International, Paper Number 981668 Detroit, MI, USA, 1998. [7] Guo Y. Q., chen, W. Q., Pao, Y. H., Dynamic analysis of space frames, The method of Reverberation-ray matrix and the orthogonality of normal modes,28. [8] Johansson, I., Edlund, S., Optimization of Vehicle Dynamics in Trucks by Use of Full Vehicle FE-Models, Göteborg, Sweden, Department of Vehicle Dynamics & Chassis Technology, Volvo Truck Corporation, 1993. The authors would like to thank the Mobarez research and industrial company, for their helpful discussions throughout the completion of this work. 21 IAU, Majlesi Branch